From the perspective of delegate math, there’s an argument to be made that the results of the New York Democratic primary will not significantly change the character of the race.
If Sanders miraculously wins, New York awards its delegates proportionally, which means that he’d still have to win the remaining states by substantial margins and convince the superdelegates, a base of Clinton support, to switch sides. That said, if Sanders does win, he can continue to make the argument that he has a viable shot at winning the Democratic nomination, that he has momentum on his side, and that he, not Clinton, has the best shot of defeating Trump.
If Sanders loses New York (which he probably will), what we’re most likely to see is a tonal transition—the race will move from being about who the most viable nominee is to who the most legitimate nominee is. The Democratic primary has become increasingly contentious over the last couple of weeks. A win in New York will solidify Clinton’s status as the only really viable nominee, in terms of delegate math, but there’s no reason to expect that she’ll then be treated as the presumptive nominee by liberals. Instead, the opposite is more likely to happen—Clinton effectively locking up the Democratic nomination will push the election into its most contentious phase, where the legitimacy of her victories and her candidacy itself becomes a focal point.